Does sorting a list by alphabetical order make sense in all languages?

I am most of the way through adding I18n to my application with the primary goal being to get it usable in Japanese as well as English. One of the functions of my website is that there are tables which when you click on the headers the column is sorted by the content which is usually alphabetical order. Now I know nothing at all about the Japanese language and I can't work out if sorting by alphabetical order is actually possible or if it actually makes sense and is useful.

Is alphabetical order as useful or possible in other languages which do not use the latin alphabet?